Peel and finely dice the shallot and garlic, and in a medium bowl, macerate in the white wine vinegar and lemon juice. Rinse, bone and finely chop the anchovies and add to the bowl. Ass the avocado flesh and mash the mixture with a fork. Whisking with the fork, gradually incorporate the olive oil and cream, as if making a think mayonnaise. Stir in the parsley, tarragon, cilantro, and basil, and add a few grinds of black pepper and pinch of salt. Taste and add more salt or vinegar if needed.